To better understand our channel modeling assumptions, we first introduce mmWave narrowband clustered channel model [1]}
\(\begin{aligned}\mathbf {h}_\mathrm {TX}&= \mathrm {vec}(\mathbf {H}_\mathrm {TX}) \\&= \mathrm {vec} \left( \sum _{l=1}^{L_\mathrm {TX}} \alpha _{\mathrm {TX},l} \mathbf {a}_\mathrm {H}(\theta _{\mathrm {TX},l},\phi _{\mathrm {TX},l}) \mathbf {a}_\mathrm {W}^\mathrm {T}(\theta _{\mathrm {TX},l},\phi _{\mathrm {TX},l}) \right) \\&= \sum _{l=1}^{L_\mathrm {TX}} \alpha _{\mathrm {TX},l} \bigg ( \mathbf {a}_\mathrm {W}(\theta _{\mathrm {TX},l},\phi _{\mathrm {TX},l}) \otimes \mathbf {a}_\mathrm {H}(\theta _{\mathrm {TX},l},\phi _{\mathrm {TX},l}) \bigg ), \\\mathbf {h}_\mathrm {RX}&= \mathrm {vec}(\mathbf {H}_\mathrm {RX}) \\&= \mathrm {vec} \left( \sum _{l=1}^{L_\mathrm {RX}} \alpha _{\mathrm {RX},l} \mathbf {a}_\mathrm {H}(\theta _{\mathrm {RX},l},\phi _{\mathrm {RX},l}) \mathbf {a}_\mathrm {W}^\mathrm {T}(\theta _{\mathrm {RX},l},\phi _{\mathrm {RX},l}) \right) \\&= \sum _{l=1}^{L_\mathrm {RX}} \alpha _{\mathrm {RX},l} \bigg ( \mathbf {a}_\mathrm {W}(\theta _{\mathrm {RX},l},\phi _{\mathrm {RX},l}) \otimes \mathbf {a}_\mathrm {H}(\theta _{\mathrm {RX},l},\phi _{\mathrm {RX},l}) \bigg ),\end{aligned}\) 
